The directed temporal graph settings form a single reachability hierarchy topped by strict and simple graphs, while undirected settings split into two incomparable strands.
Simple, strict, proper, happy: A study of reachability in temporal graphs
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Simple, Strict, Proper, and Directed: Comparing Reachability in Directed and Undirected Temporal Graphs
The directed temporal graph settings form a single reachability hierarchy topped by strict and simple graphs, while undirected settings split into two incomparable strands.